7036 Table XV. Saponification of Esters of 2,4,6-TrimethylbenzoicAcid with Potassium Hydroxide Complex of Dicyclohexyl-18-crown-6
-Concn,
Ma--
Time,
Hydrolyzed,
No.
Solvent
Ester
Ester
Base
Temp, “C
hr
Zb
1 2 3 4
Toluene Benzene Toluene Toluene Benzene Toluene Benzene
Methyl Methyl Methyl Methyl t-Butyl t-Butyl Neopentyl
0.122 0.061 0.120 0.061 0.060 0.060 0.060
0.122 0.154 0.120 0.154 0.154 0.154 0.154
73.8 f 0 . 2 8G80.1 99.9 Zk 0 . 1 105-1 11 79.680.2 104-1 11 80.3-80.7
31
58.4 39 53.0 93 22 94 40
5
6 7
5
2 5 5 5 5
The initial concentration. No saponification measurable by this method occurred when the methyl ester was refluxed at 75.5-77” with excess potassium hydroxide in 1-propanol for 5 hr. 0
oxygen fission occurs in this saponification. It is likely that the activity of these solutions of the potassium hydroxide complex of XXXI is due to the presence of unsolvated hydroxyl ions which can attack the carbonyl groups of the hindered esters much more readily than the ordinary solvated hydroxyl ions. Toxicity. Dicyclohexyl-18-crown-6 (XXXI) possesses unusual physiological properties which require care in its handling. It is likely that other cyclic polyethers with similar complexing power are also toxic, and should be handled with equal care. Oral Toxicity. The approximate lethal dose for XXXI for ingestion by rats was 300 mg/kg. In a 10day subacute oral test, the compound did not exhibit any cumulative oral toxicity when administered to male
rats at a dose level of 60 mg/kg/day. It should be noted that dosage at the ALD level caused death in 11 min, but that a dose of 200 mg/kg was not lethal in 14 days. Eye Irritation. XXXI produced some generalized corneal injury, some iritic injury, and conjunctivitis when introduced as a 10% solution in propylene glycol. Although tests are not complete, there may be permanent injury to the eye even if the eye is washed after exposure. Skin Absorption. XXXI is very readily absorbed through the skin of test animals. It caused fatality when absorbed at the level of 130 mg/kg. Skin Irritation. Primary skin irritation tests run on XXXI indicate the material should be considered a very irritating substance.
Molecular Geometry. V. Evaluation of Functions and Conformations of Medium Rings’ James B. Hendrickson2 Contribution f r o m the Edison Chemical Laboratory, Brandeis Uniuersity, Waltham, Massachusetts 02154. Receiced June 7, 1967 Abstract: Constants in the functions used for the calculation of minimum-energy conformations for n-butane and cycloalkanes were varied so as to find the set which best reproduced a dozen items of experimental data (geometry and energies). The resultant best functions were then applied to obtain the geometry and energies of the symmetrical cycloalkane rings.
alculations aimed at determining the conformational geometry of molecules3 depend for their validity the assumptions made and on the functions used to
C on
( I ) Paper I V : J. B. Hendrickson, J . Am. Chem. SOC.,86,4854 (1964). Much of the present work was the subject of a lecture by the author at the Conformational Analysis Symposium at the National Meeting of the American Chemical Society, New York, N. Y., Sept 13, 1966. Support of this work by a grant from the National Institutes of Health is gratefully acknowledged, as is the opportunity afforded the author of using the computation facilities at the Massachusetts Institute of Technology (IBM 7094) and Brandeis University (IBM 1620). (2) Alfred P. Sloan Foundation Fellow, 1962-1966. (3) A general account of the procedures involved is available in E. L. Eliel, N. L. Allinger, S. J. Angyal, and G. A. Morrison, “Conformational Analysis,” Interscience Publishers, John Wiley and Sons, Inc., Nev, York, N. Y., 1965, Chapter 7-2, which in turn derives largely from the discussions in ref 4 and 5. (4) F. H. Westheimer in “Steric Effects in Organic Chemistry,” M. S . New man, Ed., John Wiley and Sons, Inc., New York, N. Y., 1956, Chapter 12. ( 5 ) J. B. Hendrickson, J . Am. Chem. SOC.,83, 4537 (1961).
Journal of the American Chemical Society
89:26
relate geometrical parameters t o energy, Assumptions must be made partly because no clear physical mandate exists to guide the choice of selection of certain procedures and partly because the scale of the requisite computations usually demands some simplification even when employing contemporary high-speed computers. The functions used embody a number of constants, values for which are only available by extrapolation from experimental data, However, the experiments commonly either d o not measure cases comparable to those on which the functions will be used in calculations or else they are not measurements of the pure, isolated effect for which a constant is requirede6 The calculations, however, allow variations (6) For example, spectroscopic determination of angle-bending constants must involve some 1-3 nonbonded interactions’ and nonbonded potential functions are sought in many indirect ways. 3-5
December 20, 1967
7037 Table I. Geometrical Definition of Cycloalkanes Bond angles,"2*19
However, it has become increasingly clear that the angles at carbon are a function of the hybridization in effect there and that the optimum angle will not necessarily be tetrahedral but rather a function of the substituents bonded to the carbon.20 This is supported by CCC angles at methylene of around 112" (rather than 109.5 ") found experimentally for presumably "unstrained" cases such as the lower alkanes (112.5 f. 0.3 O ; see Table 111)16- l8 and cyclohexane (1 11.6 "). Thus, if the optimal angle for CCC in methylene is to be 112", those for CCH (I),) and HCH (4,) will be obtainable from the equations relating the mixing coefficients by hybridization. 2 2 It seems reasonable in fact to depend on hybridization control of the angles around the carbon and use the equations of footnote 22 to relate the CCH (I)) and HCH (4) angles to the CCC angle (e) not only for obtaining the optimum angles of each kind for the Eo minimization process above but also in actually determining I)and 6 directly from 19 for cases in which 0 differs from l12°.23 When the Westheimer force constants4 were used to evaluate a plot of E us. (e - Bo)* this plot was also found to be virtually a straight line for values of Bo between 111 and 113" and up to A0 of 10-12". The plot expressed by EO = Ke(0 - 112)2was very similar t o that obtained by the minimization procedure above, l9 with a resultant KO = 0.0215. Thus the over-all angle-bending energy for a set of six carbon resulting from either of the two approaches to interrelating 8, #, and 4 is very similar. However, the actual values of IC. and 9 obtained from 8 by the two methods differed somewhat, smaller values being obtained by the hybridization procedure. Experimental
(e,)
(19) In units of kcal/(mole deg'), Westheimer's individual constants are Kccc = 0.0175, K C C H= 0.0121, and KHCH= 0.0070. The single constant derived5 by the minimization procedure for all six angles at methylene as a function of CCC (0) alone was KO = 0.020. This is not much more than the Kccc value since the H C H constant is small and the CCH angles at methylene remain near the optimum value (109.5") as CCC and HCH are changed so that their energy contribution is small even though there are four of them. (20) The argument is lucidly presented in K. Mislow, "Introduction to Stereochemistry," W. A. Benjamin, Inc., New York, N. Y.,1964, Chapter 1. (21) M. Davis and 0. Hassel, Acta Chem. Scand., 17, 1181 (1963). (22) Following lMislow,m the hybridization indices, A * , for CH and CC bonds are related to the CCC angle (e) and HCH angle (9)
+---i-) 1
1 2
(
hence X ~ C H = (X2cc
1
+ xzEC
m
+ 3)/(X2cc COS
4 =
= 1
l + h C H
C
o
-
+ xzCc
COS
e
=
o
+
Hence, cos 9 = (cos B 1)/(3 cos B - 1). (From Figure 1, then, cos 1c. = - .\/cos 0 cos 9.) In principal, these equations only relate interorbital angles, not the internuclear angles implied in molecular geometry, but the two parallel each other so closely that these correlating equations are probably valid for either in the moderately unstrained range of interest to us here. (23) Implicit in the procedure is the maintenance of CZ,, symmetry for the methylene groups in the cycloalkane rings. In cases of severe nonbonded H-H interactions, this assumption may be incorrect and strain relief may be afforded by bending the H-C-H angle asymmetrically. However, some crude comparisons made by incorporating this distortion did not reveal much change in the total energy in cyclodecane.
Joiirnal of the American Chemical Society
+
+
1).
1
values for mean angles to hydrogens are rare, the most accurate apparently being the HCH angle at methylene in propane (see Table 111) determined by microwave spectroscopy as 106.1 f 0.2" with a CCC angle at that carbon of 112.4 f 0.2".16 The minimization process above yields 6 = 108.7" while the hybridization approach gives 6 = 106.7". Both approaches were applied in the search for best functions but only the hybridization method led to a set of functions reproducing all the empirical data and it is this method which was finally used in obtaining the values in Table I-IV. The evident correlation of hybridization and bond angle reported by Foote2* also lends support to this procedure. Variation of KO in the angle-bending energy term Eo = &(e - 1 12)2was independently carried out in the search for the most appropriate constants. In general, of course, larger values of KOtended to depress the final CCC bond angles (e) which were found and vice versa; also variations more than about f0.03 from the final value (0.0230) produced sets of cyclodecane angles inconsistent with the X-ray results. Finally, variations in KOhad differential effects on the total calculated ring energies, a moderate increase in KO (near 0.230) producing virtually no effect on the TB-cyclohexane or cyclooctane energies, a modest increase in cycloheptane and cyclononane energies, and a large increase in cyclodecane energy, The final value chosen for KO(0.0230) from these variations is only somewhat larger than that calculated via the Westheimer force constants (0.0215). After this work was completed, the author's attention was drawn to the more recent force constants of Shachtschneider and SynderZ5(average values of KccC = 0.0215, KCCH =0.0115, K H c ~ = 0.0067); when (e - 112)2 is plotted against Eo obtained from these constants and hybridization interrelation of angles, a straight-line is also obtained yielding a value of Ko = 0.025, also very close to the final value obtained in this study. Torsional Strain. Although the source of the barrier to free rotation around single bonds remains controversial, 2 6 considerable success has attended conformational calculations made by assuming the torsional strain to be a cosine function of the dihedral angle w , i.e., Et = 1/2Kt(l cos 3w), in which the constant Kt is the value (2.8 kcal/mole) for the ethane barrier. Actually, since nonbonded interactions make up a small but real portion of the ethane barrier, Kt should be somewhat less than 2.8 so that these van der Waal's forces will make up the difference. There is, however, no significant basis for using a simple cosine function here, since only the positions of maxima and minima are known, A more general expression would be the expanded form,28 Et = l/zKt(l cos 3w K,' C O S 6w), and in the search for proper functions by empirical correlation values of K,' as well as Kt were also exa m i ~ ~ e d . The * ~ results of this search provided a pre-
89:26
1
+
(24) C. s. Foote, Tetrahedron Letters, 579 (1963). (25) J. H. Shachtschneider and R. G. Snyder, Spectrochim. Acta, 19, 117 (1963). (26) E. B. Wilson, Jr., Adran. Chem. Phus., 2 , 367 (1959); for more recent discussions see ref 27 and references quoted therein. (27) R. A. Scott and H. A. Scheraga, J . Chem. Phys., 42, 2209 (1965). (28) This function retains the threefold barrier form of the simple cosine function, while introduction of cos 9 w or higher terms leads to new secondary maxima and so these were not considered.
December 20, 1967
7041
ferred value for K, = 2.65 and K,’ = 0. Thus the empirical correlation carried out here appears to support a simple cosine function for the torsional barrier. Simmons and Williams30 have recently adapted a molecular orbital treatment of Hoffman3I to provide a nonbonded H-H interaction potential “hard” enough to account for the barrier in ethane completely by nonbonded H-H interactions with no separate torsional energy term. This approach has been used before by Mason and K r e e v ~ yand ~ ~will be discussed in the next section. Nonbonded Interactions. Any pair of nonbonded atoms at an internuclear distance, r, possesses a mutual interaction, which may be cast in the form E K B = Be-”‘ - A / r 6 , the first term being a repulsive interaction, the second attractive; the constants B, p , and A are characteristic of the kind of atoms involved in the pair and the curve has a minimum (slightly attractive) at the sum of the van der Waal’s radii of the two atoms. The attractive portion of the curve (relatively large r ) may be studied reasonably accurately and acceptable values of A are available, but the repulsive potentials are very difficult to evaluate experimenta1ly.j Thus in the present work values of B and 1-1 were varied independently for both H H and CC interactions and the H C interactions were evaluated from a function the repulsive component of which was taken as the geometric mean of the H H and CC values. The interactions must be evaluated over all pairs of atoms in the molecule with the exception of the necessarily large 1-3 interactions which are presumed to be incorporated in the angle-bending terms.’ Although H-H repulsions between a few critical hydrogens account for a very large proportion of the total nonbonded interactions in most cases, the other interactions, while usually insignificant separately, take on real importance in the mass (there are 405 nonbonded interactions in cyclodecane) and may not be ignored. 3 3 In the course of the empirical correlation search, it was first found that the original function5 for H-H interactions was somewhat too soft (this arises in part because the optimum bond angles are now taken at 112” instead of tetrahedral) and the attractive component of the total nonbonded energy was too large in the larger rings owing to the rapid increase in the number of these nonbonded interactions with ring size, At first the only curves considered were also those which minimized at the sum of the traditionally quoted van der Waal’s radii of the atoms (cf, for hydrogen, 1.2-1.3 A); none of these served to provide both the energies of the rings and the angles of cyclodecane in agreement with
+
(29) Wibergls used a trial expression, Et = Kt(l cos* 3w), but this is actually identical with the simple cosine function (with K,’ = 0). (30) H . E. Simmons and J. K. Williams, J . Am. Chem. SOC.,86, 3222 (1964). (31) R. Hoffman, J . Chem. Phys., 39, 1397 (1963); Simmons and Williams actually quoted the reference to the similar work of R. M. Pitzer and W. N. Lipscomb, ibid., 39, 1995 (1963). (32) E. A. Mason and M. M. Kreevoy, J . Am. Chem. SOC.,77, 5808 (1955); 79, 4851 (1957). (33) As an example of the idea above that the simpler alkanes are not of themselves adequate tests of the various functions used in calculation, the results on the energies of cyclohexane (chair, twist-boat, and interconversion barrier) in the first paper of the series5 reproduced the experimental values about equally well whether the full set of nonbonded interactions was employed or merely the H-H potentials. This in turn suggested the validity of computing the more complex medium rings using only the few critical H-H interactions instead of the full set, 1 but the present study shows this assumption to have been in significant error in the medium rings while it was not in cyclohexane.
experimental values. The final curve (Table IV) for the H-H potential shows a minimum at 3.15 A implying a van der Waal’s radius of nearly 1.6 A for hydrogen covalently bound to carbon. These radii have been commonly assessed in the past from the intermolecular distance between hydrogens in various covalent molecules, but it may be argued that such distances are likely to be less than the minimum in the nonbonded H-H potential since the other atoms in the molecules measured are likely to have net intermolecular attraction at these distances and so squeeze the abutting hydrogens closer than their minimum-energy distance. The final curve for the important H-H potential is very similar to that offered by Bartell,’ which also reproduces most of the ring energies quite well, the Clo angles less well. These curves are also similar to the helium potentials of Amdu1-3~and to several other “soft” functions for H-H used with success in other calculations, 3+3* Potentials substantially “harder” were used by Mason and K r e e v ~ yand ~ ~ by Simmons and Williams30 in an effort to incorporate the effect of torsional strain into the H-H potential. Such functions only perform well in those cases in which there is no substantial nonbonded repulsion, such as the simple alkanes or cyclohexane (note ref 33), but fail badly where these repulsions are serious as in the medium rings; in eclipsed ethane the H-H distances are about 2.3 A so that any function which provides about 1 kcal/ mole at 2.3 A (to yield an ethane barrier of 3 kcal/mole) must be of much higher energy at the 2.0-A distances encountered in the medium rings. Cyclodecane affords an excellent qualitative test of nonbonded potential functions for H-H interactions. From Table I1 it is clear that the strain energy of cyclodecane, after subtracting bond angle bending, is 6.8 of the total 13.2 kcal/mole. There are six H-H interactions in the molecule which are critical and account for almost all of the repulsion strain: two at 1.9 A and four at 2.0 A. In the present work these alone afford 6.28 kcal/mole of total H-H energy. Hence any H-H interaction function yielding much more than about 1 kcal/mole per H-H interaction at 2.0 A cannot reproduce the strain energy of cyclodecane. Simmons’ f u n c t i ~ nrequires ~ ~ ~ ~7.4 ~ kcal/mole per H-H interaction at 2.0 A and that of Mason and Kreevoy, 6.9 kcal/mole. In summary, then, the procedure here of searching for the best assumptions (including the seven constants required by the functions) by attempting to match calculated values with empirical results for about 12 independent pieces of data has led to a very good reproduction of experimental results, as tabulated in Table I, 11, and 111, with the final selection of functions and constants used being listed in Table IV. As noted with KO above, variation of all these seven constants had differential effects on the calculated energies and angles being matched with experiment, so that the final set 273
(34) I. Amdur and A. L. Harkness, J . Chem. Phys., 22, 664 (1954); see also ref 5 . (35) F. J. Adrian, ibid., 28, 608 (1958). (36) L. R. Snvder. J . Phvs. Chem.. 67. 240 (1963). (37) A. Abe, R. L: Jernigan, and P. L: Flory, J . i m . Chem. SOC.,88, 631 (1966). (38) G. J. Gleicher and P. von R. Schleyer, ibid., 89, 582 (1967). (39) In a personal communication, Snyder36 notes that Simmons function “predicts a total H-H interaction energy in planar biphenyl of 35 kcal/mole.”
Hendrickson
1 Functions and Conformations of
Medium Rings
7042
represents a rough convergence. This convergence and the number of matched data lend strong support to the final functions of Table IV and confidence in their use in application of these conformational calculations to unknown systems. Furthermore, newer X-ray data have since offered gratifying support for these calculations in several cases described below.
Discussion of Results This paper is intended primarily to derive the preferred functions for calculation and to list the characteristics of preferred conformations. In the next paper40 are discussed the energies of methyl-substituted cycloalkanes and perspective drawings of the rings tabulated here are presented only in the next paper (with methylsubstitution energies added) to avoid duplication. Since the forms of n-butane constitute a classical model for the strain in axial ijs. equatorial methylcyclohexane, discussion of this hydrocarbon is also reserved for the second paper.40 In the third paper*l the modes of interconversion, and the energy barriers involved, are taken up for the several cycloalkanes with a view to developing a system for their conformational analysis. Although the details of geometry and energy for the various cycloalkane conformers differ somewhat from those in the previous studies'mj in no case was the stability order reversed and the qualitative discussion there is still valid. The difference in energy favoring the twist-chair form of cycloheptane over the chair is small (1.4 kcal/mole) but since the chair form represents an energy maximum on the pseudo-rotation itinerary;' it would only be expected to have a transient existence. The analogous situation is found with boat cyclohexane, which also represents a maximum on the energy profile. Evidence from nmr studies on fluorocycloheptanes supports the twist-chair form as the most stable cycloheptane conformation. 4 2 A small proportion of cycloheptane molecules should be in the twist-boat form = 2.4 kcal/mole) as a (smaller) proportion of cyclohexane is expected to be in the twistboat form. Values for the angles in a simple gem-disubstituted cycloheptane, "dimeric cycloheptanone peroxide" (I), have recently been obtained by G r ~ t hat ~Oslo ~ and show bond angles less than 1 " higher than those calculated in Table I except for the C-1 value, at the disubstituted site, which is 1.4" higher; in short, the pattern of variation in 8 parallels that in Table I but all the X-ray values are slightly higher. The dihedral angles, averaged to CZsymmetry,43differ by less than 2" from those calculated, except for os,which differs by 15", although the calculated value still lies within the range of distortion of the X-ray o3values from Cz symmetry (these show the largest distortion from symmetry, of 17"). The over-all comparison is very favorable to the accuracy of the present calculations. Cyclooctane is unquestionably the conformationally most complex cycloalkane owing to the existence of so many forms of comparable energy and this fact (40) J. B. Hendrickson, J . A m . Chem. Soc., 89, 7043 (1967). (41) J. B. Hendrickson, ibid., 89, 7047 (1967). (42) J . D. Roberts, Chemical Society Centenary Lecture, 1966; CJ Chem. Brit.,529 (1966). (43) P. Groth, Acta Chem. Scand., 18, 1801 (1964). Since publication of this preliminary account refinement has proceeded to R = 7.4 and reveals two clearly twist-chair cycloheptane rings, distorted from Cz symmetry by an average of 1 in bond angles and 10" in dihedral angles.
has caused great difficulty in the interpretation of physical data. Anet's nmr studies on cyclooctane and alkylcyclooctanes,4 4 however, are best understood in terms of the boat-chair form in consonance with the present calculations. Three X-ray studies of crystalline cyclooctane derivatives have come to light since this work was undertaken; all have the boat-chair form of the ring. The cis- and trans-cyclooctanedicarboxylic acids (I1 and 111) were examined by dun it^;^ the bond and dihedral angles down each side of the ring in each case vary on the average about 2" from average symmetrical values. The five calculated bond angles (8) in Table I are identical with those of the five average angles for the cis acid and 1-2" off for the t r a m (the observed rings themselves differ that much), while the dihedral angles vary less than 2" at each of the four positions for each ring (with one exception = 5 " ) , the calculated four angles in fact lying between the averages for the two experimental cases. The third determination is a recently completed study of "dimeric cyclooctanone peroxide" (IV) by Groth, 45 which also reveals a boat-chair conformation in both cyclooctane rings and which shows bond angles again about 1" higher than those calculated in Table I and dihedral angles 2" or less below the calculated ones. (Variations of experimental values from plane symmetry are A8 = 1.5" and A o = 3.3" on the average.)
I
I1
COOH H
O
H
I11
IV
The only previous X-ray determination of a cyclooctane was that of a salt of azacyclooctane, said to resemble an extended crown conformation after partial refinem e ~ ~ t ;subsequent *~ work9 has indicated, however, that there is too much molecular oscillation in the crystal to provide a significant structure. Over-all the experimental results to date are in remarkable agreement not only with the boat-chair form but also with the particular boat-chair geometry calculated here. Nevertheless, within 2 kcal/mole of the boat-chair form in energy exist five more symmetrical forms: chair-chair (extended crown), boat-boat (saddle), t~ist-chair-chair4~(D2), twist-boat-chair, and S I ; the latter appears somewhat preferred over the first four and is in fact the twist-tub or twist-boat of Robe r t ~ favored , ~ ~ in his work on the nmr spectra of fluorinated cyclooctanes. These six conformations of (44) F. A. L. Anet and M. St. Jacques, J . Am. Chem. Soc., 88, 2585, 2586 (1966). (45) P. Groth, Acta Chem. Scand., 19, 1497 (1965). Thc author is very grateful to Dr. Groth for the detailed geometrlcal data on this derivative, as well as that of ref 43, in advance of publication. (46) J. D. Dunitz and V. Prelog, Angew. Chem., 7 2 , 896 (1960).
Journal of the American Chemical Society 1 89:26 1 December 20, 1967
7043 nearly equal energy all represent energy minima (unlike chair cycloheptane, above) on the complex interconversion profiles discussed in the third paper41 and so there is no surprise if substitution of fluorine atoms should tip the energy balance toward the S4form. 47 With cyclononane the several C2 forms of ref 1 were reinvestigated only roughly and the best of them (TCB (47) The S4 form was not considered in the previous study’ since the system devised there for identifying all the possible symmetrical rings was created to locate only planes and axes of symmetry passing through the ring of which the S4 form (uniquely) has neither.
form in the third paper4’) found to be still about 2.2 kcal/mole less stable than the favored DBform listed here; as this parallels the previous situation, there is nothing significant t o add t o the discussion there. The same is true of other cyclodecane forms: rough calculation of the other plane- and axial-symmetric Clo conformers showed none to be preferred over the favored BCB form listed here. The all-chair (CCC) conformation is less favored by 7.5 kcal/mole. A more detailed discussion of these rings is reserved for the last paper in this group. 4 1
Molecular Geometry. VI. Methyl-Substituted Cycloalkanes’ James B. Hendrickson* Contribution f r o m the Edison Chemical Laboratory, Brandeis University, Waltham, Massachusetts 02154. Received June 7, 1967 Abstract: The strain energies of the methylcycloalkanes of six- to ten-membered rings have been computed for all
possible substituent positions on each symmetrical conformation. The results provide a basis for conformational analysis of substituted cycloalkanes.
F
or purposes of conformational analysis of the medium-ring cycloalkanes it is necessary to obtain the strain energies characteristic of substituents on the various possible positions of the several conformations of the cycloalkanes of six to ten members, In the familiar, highly symmetrical chair form of cyclohexane there are only two distinguishable positions for a substituent, i.e., equatorial and axial, implying respectively one substituent lying more or less in the plane of the ring and the other perpendicular to that plane. With less symmetrical rings the situation is made more complex by the fact that since the steric environments at the various ring carbons are different, so will the energies of the pairs of substituent positions on these carbons also differ. Thus in a ring of N carbons and no symmetry elements there will be 2N possible substituent positions. Nevertheless, models reveal that at all these atoms the equatorial-axial distinction defined above remains clear enough for this convenient nomenclature to be carried over into rings larger and less symmetrical than the chair cyclohexane. The one exception t o this procedure is the necessity of distinguishing the pair of substituents on a ring carbon lying on a twofold axis of symmetry (the axis carbon), which, by virtue of that symmetry, experience identical steric environments; such identical substituent positions, being neither axial nor equatorial, are labeled “i~oclinal.”~ The functions developed in the preceding paper for saturated hydrocarbons have been used here to evaluate the energies of methyl substituents on each possible position of the symmetrical rings determined (1) Paper V (preceding paper): J. B. Hendrickson, J . Am. Chem. SOC.,89, 7036 (1967). The author wishes gratefully to acknowledge
financial support by a research grant from the National Institutes of Health as well as the opportunity to use the computation facilities of the Massachusetts Institute of Technology (IBM 7094) and Brandeis University (IBM 1620). (2) Alfred P. Sloan Foundation Fellow, 1962-1966. (3) J. B. Hendrickson, J . Am. Chem. SOC.,86, 4854 (1964).
previously. The procedure taken is identical with that used in an earlier discussion of methylcyclohexanes and cycloheptanes4 with the exception that the newer functions were used and all nonbonded interactions (HH, HC, and CC) were included in the analysis. As before, both the CCC angle (+M) of methyl to ring carbons and the rotation (uM) of the methyl relative to a fully staggered orientation were allowed to vary independently in seeking the m i n i m ~ m . ~The optimum CCC angle (Omin) for use in the bond angle bending strain calculation for the methine carbon was taken as the mean of 112’ for methylene’ and 109.5” for C(CH&, or 110.7’, from which is derived the corresponding HCC optimum angle of 108.2”. The full equation for Eo at the methine carbon was used (eq 1) and values for Kcc = 0.0188 and KHC = 0.0129 kcal/ (mole deg2) were derived by breakdown of the over-all KO = 0.0230 derived previously for the methylene group’ (I+bM = HCC angle at methine carbon). Eo-mmethine =
Kc@
-
+
+
110.7)2 2 ( $ ~- 110.7)2] 3KHC(Ic/M - 108.2)2 (1)
This procedure has been applied to substituents on the major cycloalkane conformations with the results tabulated in Table I, the designation of substituents “down” or “up” at a given carbon when the ring is viewed from above being respectively cr and p , as in the steroid convention. The relevant views and ring numbers are shown in Chart I. The value for methylcyclohexane in the chair form ( A E = 0.7) must be compared to an average of empirical values6 showing about 1.7 kcal/mole for the (4) J. B. Hendrickson, ibid.,84, 3355 (1962). (5) 6~ was varied by 1” increments, W M by 20”. (6) A general discussion of these values is available in E. L. Eliel, N. L. Allinger, S. J. Angyal, and G. A. Morrison, “Conformational
Analysis,” Interscience Publishers, John Wiley and Sons, Inc., New York, N. Y., 1965.
Hendrickson
Methyl-Substituted Cycloalkanes
